U2, the Irish pop band, is the subject of a fascinating new documentary, "From the Sky Down," premiering Saturday on Showtime. Like most modern rockumentaries, it was commissioned by the people it is about, and it will be included in some of the versions of the 20th anniversary deluxe re-release of "Achtung Baby," coming in November. (The most deluxe of these, the Uber-Deluxe package, which costs upward of $400, also comes with a pair of sunglasses like those singer Bono wore in his guise of the Fly.) But it has been made by Davis Guggenheim, the director of "An Inconvenient Truth" and "It Might Get Loud," which featured U2 guitarist the Edge, and so comes with an air of directorial independence; it is not a thing of unadulterated self-celebration.

Indeed, if it's celebration you're after, you'd be better off renting one of the several concert films the band has issued, or "Rattle and Hum," Phil Joanou's 1988 movie about the "Joshua Tree" tour, a period of inflated earnestness that "Achtung Baby," with its dark corners, nightclub rhythms and avant-garde industrial overtones, was in part meant to puncture. Though it makes its way to a happy ending, with some laughs along the way, this is largely a story of institutional drag, communication breakdowns, false starts and failures; one of its points, illustrated with outtakes from Joanou's film, is that the same show that felt like the 90 best minutes of your life might leave the people who played it angry and depressed and thinking about making a change.

"You have to reject one expression of the band, first, before you get to the next expression," says Bono, "and in between you have nothing, you have to risk it all" — a statement so central to Guggenheim's theme that he puts it in the movie twice. He follows the group back to the Berlin studio where recording of "Achtung Baby" began in 1990, and where members will re-learn and re-think its songs (in preparation for their first appearance at Britain's Glastonbury Festival last summer) and talk about where that music came from and where it took them next.

Swapping its late investment in Americana for the twin influence of avant-garde German noise bands and Manchester dance music, U2 came to Berlin, says producer Brian Eno, to "break away for a little while and let things go out of control." Members were out to rescue "the interesting post-punk phenomenon" they had once been, in Bono's words, from the "big overblown rock band running amok" they seemed to have become.

This is a movie about getting things wrong before you get them right; you get a long look at the band's intermittently productive creative process, as stray chords and bass lines cohere into songs and the singer sings a lot of nonsense — "Bongolese," other producer Daniel Lanois calls it — on the way to mining words from melodies. "It's an odd way to live your life as a composer, building your house from the sky down" says Bono, giving the film a title.

Appropriate to its theme, "From the Sky Down" is short on full performances — mostly you get scraps of demos, old jams and new rehearsals. (You have to wait until the closing credits to see the band at Glastonbury, in a steaming start-to-finish performance of "The Real Thing"). Almost as an apology for this reticence, Guggenheim throws in new acoustic versions of "The Fly" from Bono and "Love Is Blindness" from the Edge. But it works to his dramatic advantage: When, an hour into the film, we hear "One" ("a bittersweet song about disunity") shake itself into being, the moment is physically thrilling.